L-Logistic regression models: Prior sensitivity analysis, robustness to outliers and applications

Abstract

Tadikamalla & Johnson (1982) developed the L B distribution to variables with bounded support by considering a transformation of the standard Logistic distribution. In this manuscript, a convenient parametrization of this distribution is proposed in order to develop regression models. This distribution, referred to here as L-Logistic distribution, provides great flexibility and includes the uniform distribution as a particular case. Several properties of this distribution are studied, and a Bayesian approach is adopted for the parameter estimation. Simulation studies, considering prior sensitivity analysis, recovery of parameters and comparison of algorithms, and robustness to outliers are all discussed showing that the results are insensitive to the choice of priors, efficiency of the algorithm MCMC adopted, and robustness of the model when compared with the beta distribution. Applications to estimate the vulnerability to poverty and to explain the anxiety are performed. The results to applications show that the L-Logistic regression models provide a better fit than the corresponding beta regression models.

PLreg: An R Package for Modeling Bounded Continuous Data

“…The GJS class of distributions is a particular case of the PL distributions when λ = 1. Other particular cases are the logit normal distribution (Johnson, 1949), the L-Logistic distribution (da Paz et al, 2019), and the logit slash distribution (Korkmaz, 2020), obtained by taking λ = 1 and Z as a standard normal, type II logistic, and slash random variable, respectively.…”

Power logit regression for modeling bounded data

“…The power logit class of distributions reduces to the GJS class of distributions (Lemonte and Bazán, 2016) when λ = 1 and we write Y ∼ GJS(µ, σ; r). Additionally, it leads to the logit normal distribution (Johnson, 1949), the L-Logistic distribution (da Paz et al, 2019), and the logit slash distribution (Korkmaz, 2020) by taking λ = 1 and Z as a standard normal, type II logistic, and slash random variable, respectively. The density generator function, r(z), for z ≥ 0, for the power logit normal (PL-N), power logit Student-t (PL-t (ζ) ), power logit type I logistic (PL-LOI), power logit type II logistic (PL-LOII), power logit power exponential (PL-PE (ζ) ), power logit slash (PL-slash (ζ) ), power logit hyperbolic (PL-Hyp (ζ) ), and power logit sinh-normal (PL-SN (ζ) ) follow.…”

“…The power logit regression models generalize some models: the GJS regression model (Lemonte and Bazán, 2016) is obtained by taking λ = 1; if Y i ∼ PL-LOII(µ i , σ i , 1) we have the L-logistic regression model (da Paz et al, 2019). Additionally, the model parameters are interpreted in terms of the median, dispersion and skewness of the response variable.…”

A New Quantile Regression for Modeling Bounded Data under a Unit Birnbaum–Saunders Distribution with Applications in Medicine and Politics

“…The challenges in applied regression have been changing considerably, and full statistical modeling rather than predicting just means and modes is required in many applications [24]. Some parametric quantile regression models for bounded response that are available in the literature are based on the exponentiated arcsech-normal [25], Johnson-t [26], KUMA [27], log-extended exponential-geometric (LEEG) [28], L-logistic [29], power Johnson SB [30], unit Chen (UCHE) [31], unit half-normal (UHN) [32], unit Burr-XII (UBUR) [33], and UWEI [8] distributions. Unlike regression models through the mean, quantile regression, introduced in [34], allows one to model the effect of covariates across the entire response distribution.…”

“…In this paper, we parameterize the UBS distribution in terms of its QF to evaluate the influence of one or more covariates on any quantile of the distribution of the response variable. This strategy was considered in [8,[25][26][27][28][29]47] also to model responses on the standard unit interval. Other strategies were considered in [30,48,49].…”